Report

• • • • Name: Trương Hoài Anh Email: [email protected] Facebook: Quasar Hoaianh Website: qm-for-business-class-of-mrHuy8.webnode.vn • Class email: [email protected] • Pass: qmiu12345678 Chapter 1: Introduction to Quantitative Analysis 1. Describe the quantitative analysis approach 2. Understand the application of quantitative analysis in a real situation 3. Describe the use of modeling in quantitative analysis 4. Use computers and spreadsheet models to perform quantitative analysis 5. Discuss possible problems in using quantitative analysis 6. Perform a break-even analysis Chapter 2: Probability Basic Definitions: Events, Sample Space, and Probabilities Basic Rules for Probability Conditional Probability Independence of Events Combinatorial Concepts The Law of Total Probability and Bayes’ Theorem Random variables Module 1: Game theory Two-person means there are two competing players in the game. Zero-sum means the gain (or loss) for one player is equal to the corresponding loss (or gain) for the other player. The gain and loss balance out so that there is a zero-sum for the game. What one player wins, the other player loses. Module 1: Game theory Payoff table 4 steps Row minimum Maximin Column maximum Minimax Pure vs Mixed vs Dominated strategies Expected value (EV)/saddle point Best Strategy For Player II Example 1 Player II b1 b2 a1 19 20 19 a2 5 -4 -4 19 20 Player I Column maximum Best Strategy For Player I Row minimum Maximin Payoff Minimax Payoff Example 2 Player I holds a black Ace and a red 8. Player II holds a red 2 and a black 7. The players simultaneously choose a card to play. If the chosen cards are of the same color, Player I wins. Player II wins if the cards are of different colors. The amount won is a number of dollars equal to the number on the winner’s card (Ace counts as 1.) • Establish the payoff table • Find the value of the game and the optimal mixed strategies of the players Player II Player I Red 2 Black 7 b1 b2 Black Ace a1 -2 Red 8 a2 8 1 -7 8 1 Column maximum Row minimum -2 -7 Expected value Red 2 b1 (p) Player I Black 7 b2 (1-p) EV Black Ace a1 (q) -2 1 -2p + (1-p) Red 8 a2 (1-q) 8 -7 8p -7(1-p) EV -2q + 8(1-q) q -7(1-q) • EV for q: -2q+8(1-q)=q-7(1-q) => q=15/18 • EV for p: -2p+(1-p)=8p-7(1-p) => p=4/9 • EV: -2(4/9)+(1-4/9)= -1/3 Dominated strategy • 2 players, zero-sum • At least one player has more than 2 options • Solution Payoff 4 steps Pure strategy or mixed strategy Pure => EV Mixed => elimination => EV Example 3 X1 X2 X3 Column maximum Y1 Y2 13 6 12 0 8 14 13 14 Row minimum 0 6 12 Example 3 X1 X2 X3 Column maximum Y1 Y2 13 6 12 0 8 14 13 14 Row minimum 0 12 M4.15 • ST Co. and FF Co. are both vying for more share of the market. If ST does no advertising, it will not lose any share of market if FF does nothing. It will lose 2% of market if FF invests $10,000, and it will lose 5% if FF invests $20,000 in advertising. On the other hand, if ST invests $15,000 it will gain 3% if FF does nothing; gain 1% if FF invests $10,000; and lose 1% if FF invests $20,000 in advertising. • Develop a payoff table • Find the value of the game M4.15 (sol.) Do nothing b1 ST Co. Do nothing $15,000 $10,000 $20,000 b2 b3 Row minimum a1 0 -2 -5 -5 a2 3 1 -1 -1 3 1 -1 Column maximum